Mud motors are well known for use in drilling operations. The motors can be used to locally convey power to a drill bit, such as described in GB2059481 A, GB2428212 A, and others. Mud motors can also be used to steer the bit in a desired drilling direction, such as described in WO2000037764, EP85444 A2, GB2433082 A, and to increase the rotational speed of the bit in rotary steerable systems. However, the use of a mud motor in a drill tool can cause significant and complex changes to the dynamic behavior of the tool.
In order to enhance drilling operations it is known to develop a drilling plan before drilling operations begin. Adjustments are later made to the plan based on results obtained during drilling operations. In order to develop an effective drilling plan and make appropriate adjustments in the field it is useful to have an understanding of both the formation and how a particular drilling tool operates in that formation. It is well known to use computerized modeling to simulate the operation of a particular drilling assembly for a particular formation and drilling operation. By analyzing the results of such a simulation, the drilling operation and the drilling assembly may be modified to help achieve the goals of the drilling operation. For example, results of the simulation can be analyzed to estimate vibration, efficiency, wear and other properties.
A considerable body of work has been developed around calculating the dynamic behavior of a drilling tool while drilling a borehole. However, relatively little work has been done on modeling the specific effects caused by the use of a mud motor. Moran et al, US20070185696 A1, models the kinematic aspect of the incremental rotation speed below the motor. However, there is no treatment of transient aspects of the torques and forces being transmitted between the stator and rotor. Stick-Slip and Bit-Bounce of Deep-Hole Drillstrings, A. Baumgart, Transactions of the ASME, pp. 78-82, Vol. 122, June 2000, uses a lump parameter model of the motor. However, the model neglects lateral vibrations. Further, the design of mud motors typically inhibits transmission of higher frequency vibration components upward though the drillstring, so reliance on vibration data captured above the mud motor is problematic. While it is at least theoretically possible to obtain an accurate prediction of mud motor behavior using highly complex multi-physics numerical methods such as finite elements with fluid-structure interaction, obtaining a solution at a particular instant in time can be prohibitively expensive and obtaining solutions for thousands of different configurations of the motor as required by a time transient simulation of the drill string becomes impractical.